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A suite of tools to reduce the computational effort in groundwater modeling validation and testing has been developed. The work herein explores reduction of computational effort via smart adaptivemeshing, optimization techniques, which require fewer model calls, and the development of surrogate models. Adaptive meshing reduces the computational domain by allowing for mesh refinement in areas of interest determined dynamically by the model through error indicators instead of requiring a priori knowledge or a posteriori determination and rebuilding of the computational domain. As the areas of interest change with the physics, the refinement is removed to lower computational time by using unrefinement. The computational time for dynamic mesh adaption versus uniform refinement is orders of magnitudes smaller. Further reduction in computational time may be required especially when using parameter estimation techniques that require on the order of 2n computations, where n is the number of parameters being estimated. A demonstration of the usefulness of parameter estimation techniques is given, followed by a discussion of methods to further reduce computational time. It may also be necessary to look at reduced physics-type methods to further reduce computational time for the physics-based model. Surrogate models, such as proper orthogonal decomposition (POD), greatly reduce the computational time while maintaining the most important aspects of the physics being solved. The idea here is to run the full model, create the PODs basis, then use this basis to run parameter estimation. Once a better fit has been determined, the full model is run again to capture the full-physics results. The technique is repeated as necessary to capture the “best” parameters to numerically represent the observed behavior.

A continuously variable transmission (CVT) is a type of transmission that allows an infinitely variable ratio change within a finite range, allowing the engine to continuously operate in an efficient or high performance range. A brief history of CVTs is presented, including the families under which they can be categorized. A new family of CVTs, with the classification of positive engagement, is presented. Three different published embodiments of CVTs of the positive engagement type are presented describing a meshing problem that exists apparently regardless of the embodiment in this family. The problem is called the non-integer tooth problem and its occurrences are detailed in each of the three embodiments. Specific solutions to the problem, as embodied in each case, are presented. The proposed embodiment of a new, positive engagement, continuously variable transmission is described in detail with the derived general kinematic equations of its motion. The kinematic equations for two variant embodiments are also derived. The results of the meshing analysis for this new embodiment are given and the non-integer tooth problem is exposed in three different operating conditions of the CVT. Characteristics of a solution to the non-integer tooth problem are then described, which are applicable to the positive engagement family in general.

We present a method for anisotropic mesh refinement to high-order numerical solutions. We accomplish this by assigning metrics to vertices that approximate the error in that region. To choose values for each metric, we first reconstruct an error equation from the leading order terms of the Taylor expansion. Then, we use a Fourier approximation to choose the metric associated with that vertex. After assigning a metric to each vertex, we refine the mesh anisotropically using three mesh operations. The three mesh operations we use are swapping to maximize quality, inserting at approximate circumcenters to decrease cell size, and vertex removal to eliminate small edges. Because there are no guarantees on the results of these modification tools, we use them iteratively to produce a quasi-optimal mesh. We present examples demonstrating that our anisotropic refinement algorithm improves solution accuracy for both second and third order solutions compared with uniform refinement and isotropic refinement. We also analyze the effect of using second derivatives for refining third order solutions.

ELECTROMAGNETIC ANALYSIS OF PLANAR LAYERED STRUCTURES Fatma Caliskan 169 pages Directed by Dr. Andrew F. Peterson The electrical design of microelectronic devices and their packaging is complicated because of non-ideal attributes of the actual circuit realization. Electromagnetic modeling offers the possibility of accurately predicting the electrical performance of devices and reducing the cost associated with the design process. The proposed research concerns extensions of electromagnetic modeling techniques and their application to microelectronic package design. The method of moments (MoM) is utilized as a technique in modeling and analyzing these designs. Recently, an alternate approach called the locally corrected Nystrm method (LCN) has been applied to solve integral equations in electromagnetics. Recent research suggests that the LCN is well-suited for higher-order implementations and does not require cell-to-cell current continuity in the underlying representation. Thus it may offer advantages over the MoM, especially for problems involving complex 3-D structures. If cell-to-cell continuity is not required, nonconforming meshes may offer simpler geometrical modeling. In this proposal, we consider applying the above techniques to problems in package designs, which often involve multilayer structures, solid or perforated ground planes, embedded passive devices such as capacitors and spiral inductors, and interconnects in horizontal or vertical directions. Several examples will be used to illustrate the modeling.

We present a method for anisotropic mesh refinement to high-order numerical solutions. We accomplish this by assigning metrics to vertices that approximate the error in that region. To choose values for each metric, we first reconstruct an error equation from the leading order terms of the Taylor expansion. Then, we use a Fourier approximation to choose the metric associated with that vertex. After assigning a metric to each vertex, we refine the mesh anisotropically using three mesh operations. The three mesh operations we use are swapping to maximize quality, inserting at approximate circumcenters to decrease cell size, and vertex removal to eliminate small edges. Because there are no guarantees on the results of these modification tools, we use them iteratively to produce a quasi-optimal mesh. We present examples demonstrating that our anisotropic refinement algorithm improves solution accuracy for both second and third order solutions compared with uniform refinement and isotropic refinement. We also analyze the effect of using second derivatives for refining third order solutions.

We present a method for anisotropic mesh refinement to high-order numerical solutions. We accomplish this by assigning metrics to vertices that approximate the error in that region. To choose values for each metric, we first reconstruct an error equation from the leading order terms of the Taylor expansion. Then, we use a Fourier approximation to choose the metric associated with that vertex. After assigning a metric to each vertex, we refine the mesh anisotropically using three mesh operations. The three mesh operations we use are swapping to maximize quality, inserting at approximate circumcenters to decrease cell size, and vertex removal to eliminate small edges. Because there are no guarantees on the results of these modification tools, we use them iteratively to produce a quasi-optimal mesh. We present examples demonstrating that our anisotropic refinement algorithm improves solution accuracy for both second and third order solutions compared with uniform refinement and isotropic refinement. We also analyze the effect of using second derivatives for refining third order solutions. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate